Species is a large group of living organisms that can breed freely among themselves, exchange genes and produce offspring.
Taxonomic rank is the group of living organisms that are related to each other and most basic rank is species. The lower the rank the smaller it be and contain most similar organisms.
The higher rank comprises by combining of smaller ranks like in your question the family contain many genus and order contain many families and so on. Thatswhy most higher rank would contain maximum number of species.